Test Method for Surface Figure of Large Convex Mirrors

ABSTRACT

A method of testing a convex mirror surface figure in which an optical quality substrate material is used having a convex front surface and a rear surface polished to a precise optical figure to create a lens. The lens is then tested by a standard interferometric or wavefront lens-testing method and the convex surface coated once a desired curvature is obtained. Null testing may be attained by passing a collimated interferometer beam through a focusing lens shaped to counter the predicted spherical aberration introduced by a perfect convex mirror/lens.

BACKGROUND

The invention relates generally to a method of testing the surfacequality of convex mirrors, and, in particular, to using an optical lensquality material as the mirror substrate, polishing the rear surface ofthe substrate to a precise surface figure to thereby transform it into alens, and testing this lens by standard interferometric or wavefrontmethods prior to applying a reflective coating to the convex surface.

Large convex mirrors are typically used as secondary mirrors in largereflecting telescopes. For example, the NASA 3-meter telescope on MonaKea uses a 244-mm diameter secondary mirror having a hyperbolic surfacefigure. Currently the standard method for testing convex mirrors is theHindle sphere test or the improved version, the Hindle-Simpson test. TheHindle test uses a spherical mirror that is significantly larger indiameter than the convex mirror under test and it must be perforated atits center. A diagram of the test set-up is shown in FIG. 1.

The convex mirror under test, the test optic 10, is tested at the sameconjugates as used in the telescope by employing a Hindle Sphere 11, aspherical mirror with a central perforation. The center of curvature(CoC) of the Hindle Sphere is positioned at the near focus 12 of theconvex surface under test. The diameter of the Hindle Sphere has to begreater than that of the test optic. Light from an interferometer 13 isbrought to the null test point 14 at the far focus of the convex surfaceof the test optic. After reflections off the test optic 10 and theHindle Sphere 11, the light re-traces its path back to theinterferometer 13 where it produces fringes on a monitor 15 depictingthe wavefront aberrations of the test optic.

A schematic of the Hindle-Simpson test set-up is shown in FIG. 2. Thistest makes use of a meniscus-shaped Hindle Sphere 20 and a concavecalibration mirror 21. All surfaces in the arrangement are spherical. Bydesigning the ancillary optics, in this case the meniscus-shaped HindleSphere and the concave calibration mirror, to lie close to the convexmirror under test 22, the diameters of these optics are minimized withcorresponding reduction in cost of fabrication. Nonetheless, thediameters still have to be somewhat larger than the diameter of the testoptic.

In large telescopes, astronomical or otherwise, the secondary mirroroften directs the light to a focus through a central hole in theprimary. The distance from the vertex of the secondary mirror to thisfocus can be many meters, perhaps more than 10 meters. To reduce thetotal length of the test setup, a shortening lens 30 is often used asshown in FIG. 3. The lens is often a plano-convex lens with sphericalconvex surface. Again, this lens has to have a diameter greater than thediameter of the mirror under test 31, further adding to the complexityand cost of the test setup.

There is a need for a less complex and less expensive method of testingthe surface of a convex mirror to enable accurate measurement andcharacterization of its surface figure.

SUMMARY

A new method of testing the surface figure of a convex mirror ispresented that allows a significant reduction in the complexity and sizeof the ancillary test optics, making their fabrication simpler and lessexpensive. In a preferred embodiment the convex mirror under test isfirst fabricated from a substrate material that is transmissive at thechosen test wavelength and has good optical homogeneity. The rear of themirror is polished and figured to some convenient shape so that themirror can now be tested as though it were a lens. The mirror, which maynow be refer to as a “Mirror/Lens”, can then be null tested atconvenient conjugates that are not necessarily the same as those used bythe mirror in its designed application. The combination of these threefeatures potentially allows the ancillary optics to be constructed to ahigher optical precision, which ultimately translates to more precisetesting and characterization of the convex mirror surface under test.

Other aspects and advantages of the present invention will becomeapparent from the following detailed description, taken in conjunctionwith the accompanying drawings, illustrating by way of example theprinciples of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of the Hindle sphere test set-up for testing aconvex mirror.

FIG. 2 is a schematic of the Hindle-Simpson sphere test set-up.

FIG. 3 shows the Hindle-Simpson test schematic where a shortening lensis used to reduce the total path length and produce a more compactarrangement.

FIG. 4 is a schematic of an interferometric test configuration fortesting the surface figure of a convex mirror/lens as per the presentinvention.

FIG. 5 is a schematic for testing the secondary mirror of the NASA3-meter telescope offered as one example of the present invention.

FIG. 6 is a plot of the residual wavefront aberration for a perfectlyfigured mirror/lens surface set up in double-pass as in FIG. 5.

FIG. 7A shows the fringe pattern for a perfectly figured Mirror/Lensshowing residual wavefront aberrations obtained from FIG. 5 test setup.

FIG. 7B shows the same fringe pattern as in FIG. 7A with wavefront errormagnified 50× to show the otherwise imperceptible fringe-shape details.

FIG. 8 shows a simple test set-up using an interferometer equipped witha transmission sphere.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Current methods of testing the surface quality of convex mirrors involveancillary optics that are significant larger than the mirror under test.For secondary mirrors used in large telescopes, the test set-ups arequite large since the same conjugates are used as in the actualtelescope. The present invention results in a significant reduction inthe size and complexity of the ancillary test optics, making thefabrication and assembly of these optics simpler and less expensive andenabling greater optical precision.

To act as a lens, the substrate of the convex mirror under test has tobe made from transmissive material. There are many types of glass,plastic, crystalline, and other materials from which to choose. Zeroduror fused silica might often be used because of their low thermalexpansion coefficients. The material would have to have good opticalhomogeneity so that the substrate itself does not introduce significantwavefront aberrations.

The substrate material of convex mirrors are normally ground andpolished to the required curvature and then coated with a reflectivematerial. In the present invention, the substrate material of the mirroris fabricated from a material that transmits light at the chosen testwavelength and has good optical homogeneity. The front side of thesubstrate is shaped and polished to approximately the desired convexcurvature. The rear side of the substrate is also shaped to a precisesurface figure, thereby transforming the substrate into a lens. Thesimplest rear surface figure would be an optical flat. However, thissurface could be any other spherical or aspheric, convex or concaveshape, depending on how the test is configured Iteratively testing andpolishing the test optic until a desired convex surface quality isobtained may then be carried out using a standard interferometric orwavefront lens-testing method. Once the desired convex surface isobtained, the surface is coated with a reflective material to therebyproduce the desired convex mirror.

The surface figure of this mirror/lens, referred to as the test optic,may also be tested at convenient imaging conjugates that are notnecessarily the same as those used by the mirror in its finalapplication, enabling much simpler and more compact geometries. FIG. 4shows a schematic of one test arrangement in which a standardinterferometer transmits a collimated beam 40 through a focusing lens41. The focusing lens initially converges the beam to a spot 42. Thebeam then diverges. The test optic 43 is located at a point where thediverging beam fills the test optic lens. The beam passes through thetest optic and is reflected back through the test optic by a returnmirror 44. It then passes through the focusing lens and creates a fringepattern (not shown) determined by the irregularities in the convexsurface under test. The two ancillary optics, focusing lens 41 andreturn mirror 44, may now be much smaller than the test optic. The rearsurface of the test optic 45 may be flat, concave or convex, sphericalor aspheric, depending on the configuration and shape of the returnmirror used.

Flat surfaces would normally be preferred over curved ones for costreasons, consistent with achieving satisfactory performance from theancillary optics. The next choice would be spherical surfaces, concaveor convex. Although aspheric ancillary optics surfaces are alsoenvisaged, they would only be used if there were clear benefit, such asimproving the accuracy of the test.

As an example, the testing method was applied to the 244-mm diametersecondary mirror of the NASA 3-meter telescope as shown in FIG. 5. Therequirement for this mirror is that, when combined with the 3-metertelescope primary mirror, diffraction limited performance is delivered(<λ/4 HeNe). Prior knowledge of the surface figure of the 3-meterprimary mirror had previously been established by measurement. Based onthis knowledge, NASA deemed that the ideal secondary mirror prescriptionis as follows:

Substrate material: Zerodur

Diameter: 244 mm

Radius of curvature: 1311.6 mm

Conic constant: k=−1.2068

Vertex thickness: 19.304 mm

As setup in FIG. 5, the aspheric surface 50 of the mirror/lens (testoptic) is chosen facing the return flat 51, a choice that leads tosignificantly reduced complexity of the ancillary optics. For testingother types of convex mirrors, the test optic could of course bereversed to face the other direction. In designing the test setup forthis mirror, the preferred objective is to create a null test. In a nulltest, the ancillary optics are arranged such that a perfectly figuredmirror under test would produce a null fringe pattern. A furtherobjective is to make the ancillary tests optics as small, simple andinexpensive as possible, consistent with achieving the required testaccuracy.

Although a flat return mirror 51 is shown in FIG. 5, in general there isno need to restrict to flat surfaces. If the return mirror were concaveor convex spherical as in FIG. 4, its diameter could then besignificantly smaller than the diameter of the test optic.

The layout shown in FIG. 5 comprises (on the right) a piano-convexspherical focusing lens 62 with the following specifications:

Substrate material: Fused silica

Lens type: Plano-convex (spherical)

Diameter: ˜60 mm

Clear Aperture (CA) diameter: 50.8 mm

Radius of curvature: 391 mm

Vertex thickness: 15 mm

The actual diameter of the focusing lens is chosen larger than the50.8-mm CA diameter to ensure good optical figure over CA. The lensbrings the collimated beam 53 from the interferometer to a focused spot54 at distance of 506 mm. The beam then diverges over a further 2421-mmpath to fill the 244-mm diameter Mirror/Lens under test. As shown, thedistance from the focused spot to the Mirror/Lens is exactly the same asthe focal length of the Mirror/Lens. As a result, the Mirror/Lenscollimates the light towards the 244-mm diameter return flat 51. Afterreflecting from the return flat, the beam retraces its path back intothe interferometer where it produces fringe patterns (not shown)representing the figure errors of the Mirror/Lens surface under test.

Set up as in FIG. 5, the test optic introduces a significant amount ofspherical aberration. The plano-convex-spherical focusing lens 52 istherefore designed to introduce an equal and opposite amount ofspherical aberration. The degree of compensation achieved in thedouble-pass arrangement shown in FIG. 5 is such that the testconstitutes a null test to high accuracy. Residual (uncorrected)wavefront error is less than λ/120 (HeNe). Consequently, whereas theconvex surface under test in FIG. 5 is not tested at its natural nullpoints, as it would with the Hindle Sphere test, the test is nonethelessa null test in every other sense.

Expanding on this, if the 244-mm diameter secondary test optic were tohave the ideal, perfectly figured aspheric surface (radius of curvature1311.6 mm, and conic constant −1.2068) and the rear surface wereperfectly flat, and the return mirror were also perfectly flat, and thepiano-convex-spherical lens surfaces were also perfectly figured, theresidual double-pass wavefront aberration would be less than λ/120(HeNe) as shown in FIG. 6.

The fringe pattern corresponding to the FIG. 6 double-pass wavefrontaberration is shown in FIG. 7A. FIG. 7B is a 50× magnified view of theFIG. 7A fringes. The fringes in FIG. 7A look almost perfectly straightindicating an extremely well figured test optic convex surface. Ofcourse, by use of more sophisticated ancillary optics, residualwavefront aberration could be reduced further, or eliminated altogether,so that a true null fringe pattern could be obtained.

If an interferometer producing the collimated beam 81 is equipped with atransmission sphere 82, in principle, the only additional requirement totest a convex mirror 83 would be to polish the rear surface flat 84 sothat this surface acts as the return flat. Such an arrangement is shownin FIG. 8.

Generally, the transmission reference sphere does not compensate forspherical aberration generated by the double-pass through test opticTransmission spheres generally provide near-perfect spherical wavefrontsentirely free of any sort of spherical aberration. Therefore, it is notusually possible to use the FIG. 8 arrangement as a null test. Tested asin FIG. 8, a perfectly figured convex surface of the test optic wouldproduce a non-zero but predicable wavefront error. If predictedwavefront error data were subtracted from the measured fringe pattern, apseudo-null fringe pattern would result.

Interpretation of Fringe Patterns and Assessment of Surface Figure Error

For a mirror surface tested in reflection, a surface height error, H,produces wavefront error, W, as follows:

W=2H   (1)

When the same surface is tested in transmission, as in a lens, exactlythe same surface height error, H, gives rise to wavefront error, W,given by

W=(n−1)H   (2)

where n is the refractive index of the substrate material used to makethe mirror.

For many types of glass, n is about 1.5 but other glass types haverefractive indices greater than 2. For crystalline substrates, n may beeven higher. For Zerodur, as used in the FIG. 5 setup, n=1.54 at HeNe(633 nm). Equation (2) then becomes

W=0.54H   (3)

In the FIG. 5 test, the beam passes through the fused silica Mirror/Lenstwice. In this case the wavefront error is given by

W=2.(n−1)H=1.08H   (4)

Comparison of Equations (1) and (4) indicates that the test methoddescribed in this disclosure is about 2 times less sensitive than is thecase when mirrors are tested in reflection. To illustrate thedifference, for a 1-micron surface height irregularity, under thestandard test in reflection described by Equation (1), we should expectto see 2H/λ≈3.2 fringes (HeNe). Under the Mirror/Lens test (Equation 4)we should expect to see 1.08H/λ≈1.75 fringes (HeNe).

With the Hindle Sphere test illustrated in FIG. 1, the beam tworeflections off the convex mirror under test. For this case, wavefrontaberration, W, is given by

W=4H   (5)

The test sensitivity of the present invention is about 1.85× less thanthat of a standard mirror interferometric test where there is asingle-reflection (c.f. Equations 1 and 4). The test sensitivity of thepresent invention is about a 3.7× less than that of a Hindle Spherewhere there are two reflections from the mirror surface under test (c.f.Equations 4 and 5).

From the foregoing it will be appreciated that the convex mirror testingmethod of the present invention employs smaller diameter and lessexpensive ancillary optical components. The method further provides anull testing method that may be set up at convenient conjugatedistances.

1. A method for producing a convex mirror having a desired surfacequality wherein the mirror under test, the test optic, is treated as alens prior to applying a reflective coating to the convex surface of thetest optic substrate comprising the steps of: a) choosing an opticallens quality material for the test optic substrate, the test optichaving a front convex surface side and a rear side; b) polishing therear side of the test optic to a precise surface figure, therebytransforming the test optic into a lens; c) iteratively testing andpolishing the test optic until a desired convex surface quality isobtained using a standard interferometric or wavefront lens-testingmethod; and d) once the desired convex surface is obtained, coating theconvex surface with a reflective material to thereby produce a desiredconvex mirror.
 2. The method of claim 1, wherein the precise surfacefigure of the rear side of the test optic is an optical flat.
 3. Themethod of claim 1, wherein the precise surface figure of the rear sideof the test optic is a spherical convex or concave shape or an asphericconvex or concave shape.
 4. A method for testing the optical surfacequality of a convex mirror, the test optic, wherein the test optic isfirst transformed into a lens and tested prior to applying a reflectivecoating to the convex surface of the test optic substrate comprising thesteps of: a) choosing an optical lens quality material for the testoptic substrate, the test optic having a front convex surface side and arear side; b) polishing the rear side of the test optic to a preciseoptical flat surface, thereby transforming the test optic into a lenswith the rear optical flat surface acting as a return mirror; c) passinga collimated beam from an interferometer through a transmission sphereproducing near-perfect spherical wavefronts that pass through both frontand rear surfaces of the test optic, are reflected back from a returnmirror, back through both surfaces of the test optic, and then backthrough the transmission sphere to produce a wavefront error measurementof the front convex surface; and d) determining the test optic convexsurface error by subtracting a predicted wavefront error based on adesired test optic convex surface from the measured wavefront error. 5.A null-testing method for determining the optical surface quality of aconvex mirror wherein the mirror under test, the test optic, is treatedas a lens prior to applying a reflective coating to the convex surfaceof the test optic substrate comprising the steps of: a) choosing anoptical lens quality material for the test optic substrate, the testoptic having a front convex surface side and a rear side, the desiredconvex surface having in general an aspherical curvature that introducesa spherical aberration that can be pre-calculated when tested atconjugates other than those intended in its final application; b)polishing the rear side of the test optic to a precise optical surface,thereby transforming the test optic into a lens; c) passing a collimatedbeam from an interferometer through a focusing lens designed tointroduce an equal and opposite amount of spherical aberration to thatcalculated for the desired test optic and to fill the test optic lenswith the interferometer beam, through both front and rear surfaces ofthe test optic, being reflected back from a return mirror, back throughboth surfaces of the test optic, and then back through the focusing lensto form a null interference pattern if the test optic has the desiredconvex surface.